DON'T take the HEX (or even the HEC) as it puts you in an area of London from where you need an additional Tube ride to get to anything interesting.

Get a 1 day travelcard and take the Tube to Hammersmith, walk across the platform and take a District or Circle Line Tube to Westminster.

Exit through the Bridge Street exit and gawp.

After that in the immediate area you have The London Eye, Houses of Parliament, Westminster Abbey, Cabinet War Rooms, Whitehall, Downing Street, Horse Guards (the shiny men in Whitehall are interesting) Trafalgar Square, National Gallery, National Portrait Gallery and it's a little stroll down to Buckingham Palace